Abstract
This chapter focuses on the pythagorean and heronic triples. The well-known relationship between the hypotenuse and the other two sides of a right-angled triangle, x2 + y2 = z2, can be considered as an indeterminate equation with three unknowns. The chapter explains that pythagorean triples are a particular case of Heronic Triples; the name for three integers expressing the lengths of the sides of a triangle with an integral area. It is easy to prove that any of the altitudes of a Heronic triangle give two right-angled triangles with rational sides, either adjacent or overlapping each other. By causing the identical sides of the triangles to become common to each other, two triangles with rational sides can be obtained.
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